6. Fractional Order Filter Discretization by Particle Swarm Optimization Method

Fractional-order filter functions are generalization of rational filter functions, which includes integer order filter functions. Fractional-order filters present advantages of more options in frequency selectivity properties of filters compared to integer order counterparts. This study presents an application of Particle Swarm Optimization (PSO) for IIR filter discretization of fractional-order continuous filter functions. The proposed method enforces particles to search in stable filter search regions and ensures the stability of optimized IIR filter functions that approximate to amplitude response of continues fractional-order filter functions. In this chapter, illustrative filter discretization examples are demonstrated to show results of PSO algorithm and these results are compared with results of Continued Fraction Expansion (CFE) approximation method. Stop band approximation performance is very substantial for band reject filter design. We observed that proposed discretization method can provide better approximation to the amplitude response of fractional-order filter functions at the stop bands compared to CFE approximation method.